Any mechanically driven resonant system has an inherent “quality factor” or “Q”, that defines some aspect of the way the resonant system reacts to stimuli. The quality factor of certain resonant systems can be controlled and/or adjusted, for example electronically.
One exemplary mechanically-driven resonant system that can be Q-controlled is the cantilever portion of a scanning probe force microscope. When the microscope is operating in its AC mode, the driving amplitude and driving phase of the device can be adjusted. The effect of such an adjustment is to make the cantilever system behave as if it had a higher or lower Q than would naturally occur within the system.
FIG. 1 illustrates how an analog based implementation of Q control can be carried out. Circuit 100 is part of a control system for an atomic force microscope. A cantilever 105 has a tip 110 that contacts an item of interest. The cantilever is driven in AC mode via a piezoelectric based actuator 115. In a system with an optical detector, a laser or other optical source 120 projects a laser beam 122 on the cantilever. A reflection 124 based on the projected laser beam is reflected by a mirror 125 to a detector 130 that produces an output signal indicative of the position of the cantilever tip. For example, the detector may include, as shown, a split position detector 132 that detects deviation from its center. The output signal 133 of the detector represents the amount by which the cantilever tip has changed position. The signal 133 is sent to a lock-in amplifier 135 which also receives the output of a function generator 140 that drives the actuator 115.
In order to change the effective Q of the system, the output signal 133 is phase shifted by a variable phase shifter 145 which produces a 90 degree phase shift, and then multiplied by an amplitude gain by gain amplifier 150. The amplitude gain may be positive in order to damp the Q, and negative to enhance the Q. The resultant Q adjusting signal 155 is added by an adder 160, to the driving wave formed by the function generator 140.
This analog phase shifting circuit includes analog components which may be frequency dependent. Moreover, the resonant frequency may be based on characteristics of the specific cantilever, and the way the cantilever is used. Therefore, changing to a new cantilever may change the resonant frequency of the system. Also, characteristics of the medium in which the cantilever is used, such as in air versus in fluid, will change the resonant frequency of the system. This resonant frequency change must be compensated in the phase shift circuit 145 to insure a 90 degree phase shift between the signal from the cantilever position detector and the signal 155 that is added to the drive.
The phase shifter 145 is shown as an adjustable phase shifter. This kind of Q adjustment usually requires changing a manually-adjustable value, to change the circuit values of some aspect of the analog phase shift. This adjustment is made to ensure a 90 degree phase shift for the new resonant frequency.
Another possible disadvantage of the analog phase shift circuit is that analog phase shifters typically operate only over a limited range of frequencies. In order to phase shift a wideband signal, several different phase shifters may be used in tandem.
The analog implementation also requires a multiplier to effect the analog gain. For example, this may be a voltage controlled analog amplifier, or a digitally controlled analog amplifier. However, circuits of this type may add noise to the output signal 133, and thereby corrupt the effectiveness of the Q control.